COMMON MULTIPLES AND FACTOR

Factors: The factor of a number is the whole number that divides the number exactly. For example, the factors of 18 may be found as follows;

                     18 = 1 x 18

                     = 2 x 9

                     = 3 x 6

Multiples: A multiple of a number is obtained by multiplying it by any whole number. For example, the multiples of 4 are 4, 8, 12, 16, 20, 24 etc.

A prime number is a number that can only divide itself. It has only two factors which are 1 and itself. Examples of prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, etc.

Example: (a) find all the factors of 18

               (b) State which of these factors is even

                 (c) state which of these factors are prime numbers

               (d) Write the first three multiples of 18

Solution

(a)    Factors of 18 are 1, 2, 3, 6, 9, and 18

(b)   The even numbers are 2, 6, and 18

(c)    The prime numbers are 2 and 3

Example 1: Find the factor of 56

Solution:

1 × 56

2 × 28

4 × 14

7 × 8

Therefore 56 = 1, 2, 4, 7, 8, 14, 28, and 56.

 Product of Prime Factors.

Example 2: Express 56 and 108 as the product of prime factors in index notation.

Solution:

56 = 2 × 2 × 2 × 7 = 23 x 7

108 = 2 × 2 × 3 × 3 × 3 = 22 x 33

Note that the numbers must be a prime numbers